Theorems · Theorem · functional analysis
Seminorm.mem_ball_zero
∀ {𝕜 : Type u_3} {E : Type u_7} [inst : SeminormedRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : SMul 𝕜 E]
(p : Seminorm 𝕜 E) {y : E} {r : ℝ}, y ∈ p.ball 0 r ↔ p y < r- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- AddCommGroupstatement and proof · cited by 12,871
- sub_zeroproof · cited by 938
- SeminormedRingstatement and proof · cited by 446
- Seminormstatement and proof · cited by 272
- Seminorm.ballstatement · cited by 78
- Seminorm.mem_ballproof · cited by 10
Cited by11
Results whose statement or proof uses this declaration.
- Seminorm.ball_zero_eqproof · cited by 7
- Seminorm.smul_ball_zeroproof · cited by 5
- Seminorm.absorbent_ball_zeroproof · cited by 4
- Seminorm.balanced_ball_zeroproof · cited by 3
- Seminorm.ball_zero_absorbs_ball_zeroproof · cited by 3
- WithSeminorms.isVonNBounded_iff_finset_seminorm_boundedproof · cited by 2
- Seminorm.gauge_ballproof · cited by 2
- Seminorm.absorbent_ballproof · cited by 1
- SeminormFamily.basisSets_smul_rightproof · cited by 0
- SeminormFamily.basisSets_zeroproof · cited by 0
- Seminorm.ball_norm_mul_subsetproof · cited by 0